Washington (CNN) -- President Barack Obama took a victory lap Tuesday on his signature domestic achievement -- health care reform -- by hosting a "tele-town hall" meeting in Maryland timed to coincide with first mailing of prescription drug rebate checks to older Americans.

The administration has held frequent meetings in recent weeks to tout the various aspects of the nation's new health care law to senior citizens. Portions of the law take effect this year.

"This health care bill alone doesn't solve all our problems and I don't want to overadvertise," Obama said. But it will lead to the enactment of a number of key reforms that will make the overall health care system more efficient and effective over time, he asserted.

The first checks will be sent Thursday, three weeks earlier than scheduled, to about 80,000 people.

Medicare has sent out brochures reminding seniors they don't have to fill out a form to receive the benefit, nor should they give out personal information -- such as Social Security or bank account numbers -- to anyone who calls about the checks.

The rebates are the first step to close the gap in Medicare's prescription drug coverage. The Department of Health and Human Services estimates that about 4 million seniors will get the rebates in 2010.

The move is one of the first tangible results of the health reform law. At a news conference last month, Health and Human Services Secretary Kathleen Sebelius said closing the donut hole is "one of the biggest ways the new law is going to help seniors."

Seniors get stuck in the donut hole when their prescription drug expenses exceed the amount that can be paid for through basic Medicare coverage, but aren't enough to qualify for catastrophic coverage. Under the new health care law, the donut hole should be completely closed by 2020.

"We think our members will see these checks as a good faith down payment on what they've been looking for so long: closing this coverage gap," said Cheryl Matheis, AARP's senior vice president for health strategy.

"Many Medicare patients are on a fixed income, so every dollar helps," she added.